Autler-Townes spectroscopy of a Rydberg ladder

TL;DR

This work tackles the challenge of locating and stabilizing two-photon Rydberg resonances in inverted ladder schemes where Doppler broadening suppresses EIT. It introduces the two-photon Autler-Townes resonance (TPAT) observed on the upper-leg, which yields a higher signal-to-noise ratio and resolves resonances up to $n=80$ (vs. $n\approx54$ for EIT). By employing modulation transfer spectroscopy, TPAT also provides an effective error signal to lock the upper-leg laser, with a lock capture range exceeding $8\ \mathrm{MHz}$ and tunable width via lower-leg intensity. Overall, TPAT offers a robust spectroscopy and laser-stabilization approach for inverted two-photon excitation in hot vapors, enabling precise spectroscopy of high-$n$ Rydberg states and practical frequency references.

Abstract

Ladder-type two-photon excitation of an atom from a ground state $|g\rangle$, to an intermediate excited state $|e\rangle$, and, finally, to a Rydberg state $|r\rangle$, has a variety of uses from quantum information to sensing. A common scheme for detecting this transition optically is through electromagnetically induced transparency (EIT). However, in inverted wavelength schemes, where the ground-to-excited transition wavelength is shorter than the excited-to-Rydberg transition wavelength, the strength of the EIT feature on the lower-leg beam is strongly reduced in a Doppler-broadened medium. Here, we report on an alternative two-photon spectroscopic feature, which we term the two-photon Autler-Townes resonance, observed on the upper-leg beam. Compared to the EIT signal, this feature's superior signal-to-noise ratio allows one to resolve Rydberg resonances with principal quantum number as high as $n=80$. We also show that such a feature can be utilized to generate an error signal for stabilizing the frequency of the upper-leg beam.

Figures (5)

• Figure 1: (a) Effective three level model. 420 nm light with Rabi frequency $\Omega_{\mathrm{l}}$ couples the ground and intermediate state. 1012--1026 nm light couple the intermediate state to a range of Rydberg states with Rabi frequency $\Omega_{\mathrm{u}}$. The intermediate state decays with rate $\Gamma_{\mathrm{l}}$, and the Rydberg state decays with rate $\Gamma_{\mathrm{u}}$. (b) Simulated absorption of weak lower-leg light when the detuning of the strong upper-leg driving light is scanned (top) and resultant transmission $T_\mathrm{l}$ (bottom) obtained via integrating over all velocity classes. (c) Simulated absorption of the weak upper-leg light with strong lower-leg driving light (top) and resultant transmission $T_\mathrm{u}$ (bottom) obtained via integrating over all velocity classes and scanning $\delta_u$. The dashed lines in the top plot denote tangential cuts that can be drawn at the turning point of the signal. Parameters used: $n=30$, $\Gamma_{\mathrm{l}} = 2\pi \times 1.4$ MHz, $\Gamma_{\mathrm{u}} = 2\pi\times11$ kHz, $T=89^\circ$C; $\Omega_{\mathrm{l}} = 2\pi \times 40$ kHz and $\Omega_{\mathrm{u}} = 2\pi \times 1.2$ MHz in (b); $\Omega_{\mathrm{l}} = 2\pi \times 4.8$ MHz and $\Omega_{\mathrm{u}} = 2\pi \times36$ kHz in (c). Atomic values obtained from the Alkaline Rydberg Calculator arc.
• Figure 2: (a) Overview of the experimental apparatus. Inset denotes the profile of the lower-leg beam (blue) and the upper-leg beam (red). (b) Measured upper-leg transmission $T_\mathrm{u}$ with TPAT signal. The lower-leg beam is resonant with the $^{87}$Rb $\ket{5S_{1/2},\text{ }F=2} \rightarrow \ket{6P_{3/2}, \text{ }F'=3}$ hyperfine transition at zero velocity. The upper-leg beam is scanned across the two-photon resonance of the Rydberg state. (c) Measured lower-leg transmission $T_\mathrm{l}$ with EIT signal. The lower-leg detuning is scanned across the $^{87}$Rb $\ket{5S_{1/2},\text{ }F=2} \rightarrow \ket{6P_{3/2}, \text{ }F'=3}$ hyperfine transition while the upper-leg beam is resonant with the $^{87}$Rb $\ket{6P_{3/2}, \text{ }F'=3} \rightarrow \ket{30S_{1/2}}$ transition. Inset denotes the EIT peak. The vapor cell is held at $89^{\circ}$C.
• Figure 3: (a) Rms noise of the lower-leg single-photon absorption over various optical densities. The rms noise is obtained via taking the square root of the integrated noise power spectral density of the photodiode output over a bandwidth of 400 kHz, corresponding to the average transit time of the atoms through the beam. Dashed line corresponds to fit (described in the text). (b) rms noise as a function of beam waist at fixed optical density. Dashed line corresponds to fit (described in the text).
• Figure 4: (a) Measured and ideal signal-to-noise ratio as a function of Rydberg level for TPAT and EIT features. For TPAT the intensity at the center of the lower-leg beam is 67 $\mathrm{mW}/\mathrm{mm}^2$ at the cell input and focuses down to 120 $\mathrm{mW}/\mathrm{mm}^2$ at the output, while the upper-leg is held at 10 $\mathrm{mW}/\mathrm{mm}^2$. For the EIT signal, the intensity at the center of the lower-leg beam is 2.8 $\mathrm{mW}/\mathrm{mm}^2$ at the input and 5.0 $\mathrm{mW}/\mathrm{mm}^2$ at the output, with the upper-leg held at 170 $\mathrm{mW}/\mathrm{mm}^2$. The measurement bandwidth is 1 MHz. (b) Measured TPAT feature traces for various $n$ levels. (c) Measured EIT feature traces for various $n$ levels.
• Figure 5: Measured error signal from modulation transfer spectroscopy with a bandwidth of 1 MHz for the Rydberg state $n=30$ at vapor cell temperature $88^\circ$C.